Formally, DFT employs a doubled coordinate system, \(x^{A}=(\tilde{x}_{\mu },x^{\nu })\) , and subsequently unifies diffeomorphisms and \(B\) -field gauge symmetry. Yet, the geometry is not truly doubled: half of the coordinate dependency should be turned off e.g. by setting \({\scalebox {1.1}{{\frac{\partial ~}{\partial \tilde{x}_{\mu }}}}\equiv 0}\) , up to \(\mathbf {O}(D,D)\)  rotations. This may suggest that half of the doubled coordinates are actually gauged [1]}. By gauging e.g. \(\tilde{x}_{\mu }\)  explicitly as \({\rm D}x^{A}=\big ({\rm d}\tilde{x}_{\mu }-A_{\mu },{\rm d}x^{\nu }\big )\) , it is possible to define an \(\mathbf {O}(D,D)\) -symmetric proper length [2]} by means of the corresponding pull-back of the generalised metric \({\rm D}x^{A}{\rm D}x^{B}{\cal H}_{AB}\) , and to further construct `doubled-yet-gauged' actions for particles [3]} and strings [4]}, [5]}. When the generalised metric is \((0,0)\)  Riemannian, all the components of the auxiliary gauge connection \(A_{\mu }\)  appear quadratically in the actions. After integrating them out, one recovers the conventional particle and string actions. On the other hand, when the background is non-Riemannian, \({n+{\bar{n}}}\)  components come out linearly to play the role of Lagrange multipliers. Consequently, the particle is frozen with identically vanishing proper velocities over the non-Riemannian \((n+{\bar{n}})\) -dimensions. Further, the string becomes chiral over the \(n\) -directions and anti-chiral over the \({\bar{n}}\) -directions [6]}, as happens in the \((1,1)\)  non-relativistic string case [7]}. This also implies that, at the classical level, chiral strings get frozen too [8]}.
